Do particles ever touch each other during a collision?
'Touching' is an ill-defined concept in physics as you've correctly pointed out. Perhaps by "touch" you mean "overlap" then yes if interacting particles are quantum mechanical objects then they have some associated wavelength which may overlap/interfere with another particle.
Another thing I've read about is, the closer the particles get to each other the greater the density of virtual particles until they reflect or particle pair creation occures due to the high energy density. If true, how does that work?
Let's consider the EM force, where this is well-defined. The EM force is mediated by the exchange of photons (particles of light). This means that a charged particle, such as an electron, is composed of not only itself but also a field of photons.
Let's imagine one electron, which I will refer to as the 'hard' electron. The hard electron emits a photon from it's field which will return to the electron in order to preserve energy/momentum. The photon can effectively act however it likes before it returns to the electron. It can for example split into an electron/anti-electron pair. However the electron/anti-electron must recombine to produce the photon which must return to the hard electron so that it can still preserve energy/momentum. Because the EM field strength increases at smaller distances with respect to the hard electron, there are more photons and so there is more opportunity for an interacting particle to interact with the electron/anti-electron pair.